The Dynamic Response to Impact Loading of a Fluid-Supported Rectangular Plate

Abstract

This work considers the elastodynamic response of a rectangular plate supported by a fluid on one side, and subjected to impact loading on the other side. The presence of the fluid in our problem has the effect, first, of lowering the natural frequency of the plate due to the increased inertia, and secondly, of damping its vibrations owing to the energy carried off in the form of sound waves. The deflection of the plate is approximated by a double infinite series in the spatial coordinates. Each term of the series consists of a product of two modes of deflection of beams, having the same boundary conditions as the plate, multiplied by a time dependent function. The problem is solved for various combinations of fluids, impact loadings, geometrical configurations, and boundary conditions. Excellent agreement is obtained between the present results for eigen frequencies and the static deflections in vacuo and published results. Furthermore, good agreement is obtained for the added-mass and the damping magnitude. As for the dynamic case, since no complete solutions are available, the present results are at least shown to be self-consistent.